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Fuzziness, Probability, Uncertainty and the Foundations of Knowledge

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On Fuzziness

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 299))

Abstract

This paper will describe how fuzzy logic, neural networks and other fundamental approaches to the nature of knowledge and epistemology fit together, both at a philosophical level and at the level of practical technology. The views herein are my own, but the bulk of the credit really belongs to Lotfi Zadeh and to the unusual, rich dialogue he has created through the Berkeley Initiative for Soft Computing (BISC). Only this very special kind of dialogue can really bring out the many cross-connections which exist in these complex fields of research. Lotfi has done an amazing job of pushing the community just hard enough, through clear but tricky questions, to get ever deeper into a wide range of issues related to fuzzy logic and to soft computing in general.

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References

  1. Albus, J.S.: Outline for a Theory of Intelligence. IEEE Transactions on Systems, Man and Cybernetics 21(2), 473–509 (1991)

    Article  MathSciNet  Google Scholar 

  2. Barron, A.R.: Universal Approximation Bounds for Superpositions of a Sigmoidal Function. IEEE Transactions on Information Theory 39(3), 930–945 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barron, A.R.: Approximation and Estimation Bounds for Artificial Neural Networks. Machine Learning 14(1), 113–143 (1994)

    Google Scholar 

  4. Box, G.E.P., Jenkins, G.M.: Time-Series Analysis: Forecasting and Control. Holden-Day, San Francisco (1970)

    MATH  Google Scholar 

  5. Deutsch, K.W.: Nationalism and Social Communications, 2nd revised edn. MIT Press, Cambridge (1966)

    Google Scholar 

  6. Deutsch, K.W.: The Nerves of Government. Glencoe, New York (1967)

    Google Scholar 

  7. Feldkamp, L.A., Prokhorov, D.V.: Recurrent Neural Networks for State Estimation. In: Proceedings of the Workshop on Adaptive and Learning Systems, Narendra edn. Yale University (2003), Posted with permission at http://www.werbos.com/FeldkampProkhorov2003.pdf

  8. Fogel, D.B., Hays, T.J., Han, S.L., Quon, J.: A Self-learning Evolutionary Chess Program. Proceedings of the IEEE 92(12), 1947–1954 (2004)

    Article  Google Scholar 

  9. Gödel 1944:126 footnote 17: “Russell’s mathematical logic” appearing in Kurt Gödel: Collected Works: vol. II Publications 1938-1974. Oxford University Press, New York (1944)

    Google Scholar 

  10. Ilin, R., Kozma, R., Werbos, P.J.: Beyond Backpropagation and Feedforward Models: A Practical Raining Tool for more Efficient Universal Approximator. IEEE Transactions on Neural Networks 19(3), 929–937 (2008)

    Article  Google Scholar 

  11. Johnstone, I.M.: Statistical Challenges of High-dimensional Data. Philosophical Transactions of the Royal Society, Mathematical, Physical and Engineering Sciences 367(1906), 4237 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lewis, F.L., Liu, D.: Reinforcement Learning and Approximate Dynamic Programming for Feedback Control. Wiley (2012)

    Google Scholar 

  13. Liang, J., Venayagamoorthy, G.K., Harley, R.G.: Wide-Area Measurement based Dynamic Stochastic Optimal Power Flow Control for Smart Grids with High Variability and Uncertainty. IEEE Transactions on Smart Grid 3(1), 59–69 (2012)

    Article  Google Scholar 

  14. Morris, C.N.: Parametric Empirical Bayes Inference: Theory and Applications. Journal of the American Statistical Association 78(381), 47–55 (1983), Article Stable http://www.jstor.org/stable/2287098

    Article  MathSciNet  MATH  Google Scholar 

  15. National Science Foundation, Emerging Frontiers in Research and Innovation (2008), http://www.nsf.gov/pubs/2007/nsf07579/nsf07579.pdf

  16. Príncipe, J.C., Euliano, N.R., Curt Lefebvre, W.: Neural and Adaptive Systems: Fundamentals through Simulations. Wiley, New York (2000)

    Google Scholar 

  17. Prokhorov, D.V.: Prius HEV Neurocontrol and Diagnostics. Neural Networks 21(2-3), 458–465 (2008)

    Article  Google Scholar 

  18. Raiffa, H.: Decision Analysis. Addison-Wesley, Reading (1968)

    MATH  Google Scholar 

  19. Schumann, J.M., Yan, L. (eds.): Applications of Neural networks in High Assurance Systems. Springer, Berlin (2010)

    MATH  Google Scholar 

  20. Si, J., Barto, A.G., Buckler Powell, W., Wunsch, D. (eds.): Handbook of Learning and Approximate Dynamic Programming. IEEE Press Series on Computational Intelligence. Wiley-IEEE Press (2004)

    Google Scholar 

  21. von Neumann, J., Morgenstern, O.: The Theory of Games and Economic Behavior. Princeton U. Press, Princeton (1953)

    Google Scholar 

  22. Walls, D.F., Milburn, G.J.: Quantum Optics. Springer, New York (1994)

    MATH  Google Scholar 

  23. Werbos, P.J.: Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences, Ph.D. Thesis, Committee on Applied Mathematics, Harvard U. (1974); reprinted in its entirety in [27]

    Google Scholar 

  24. Werbos, P.J.: Building and understanding adaptive systems: A Statistical/Numerical Approach to Factory Automation and Brain Research. IEEE Transactions on Systems, Man and Cybernetics 17(1), 7–20 (1987)

    Article  Google Scholar 

  25. Werbos, P.J.: Rational Approaches to Identifying Policy Objectives. Energy: The International Journal 15(3/4), 171–185 (1990)

    Article  Google Scholar 

  26. Werbos, P.J.: Econometric Techniques: Theory Versus Practice. Energy: The International Journal 15(3/4), 213–236 (1990)

    Article  Google Scholar 

  27. Werbos, P.J.: The Roots of Backpropagation: From Ordered Derivatives to Neural Networks and Political Forecasting. Wiley (1994)

    Google Scholar 

  28. Werbos, P.J.: Elastic Fuzzy Logic: A Better Fit to Neurocontrol and True Intelligence. Journal of Intelligent and Fuzzy Systems 1, 365–377 (1993); reprinted and updated in Gupta, M. (ed.): Intelligent Control. IEEE Press, New York (1995)

    Google Scholar 

  29. Werbos, P.J.: Backwards Differentiation in AD and Neural Nets: Past Links and New Opportunities. In: Bucker, H.M., Corliss, G., Hovland, P., Naumann, U., Norris, B. (eds.) Automatic Differentiation: Applications, Theory and Implementations, Springer, New York (2005), Posted at http://www.werbos.com/AD2004.pdf

    Google Scholar 

  30. Werbos, P.J.: Bell’s Theorem, Many Worlds and Backwards-Time Physics: Not Just a Matter of Interpretation. International Journal of Theoretical Physics 47(11), 2862–2874 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Werbos, P.J.: Intelligence in the Brain: A Theory of How it Works and How to Build it. Neural Networks 22(3), 200–212 (2009)

    Article  Google Scholar 

  32. Werbos, P.J.: Neural Networks and the Experience and Cultivation of Mind. In: Neural Networks (special issue based on IJCNN 2011, published electronically, hard copy in press) (2012)

    Google Scholar 

  33. Werbos, P.J.: A Three Step Program For Return To Reality. Problems of Nonlinear Analysis in Engineering Systems, an International IFNA-ANS Journal (in press, 2012), a preliminary draft is posted at http://www.scribd.com/doc/80026749/ThreeStep-v5

  34. Werbos, P.J.: Solitons for Describing 3-D Physical Reality: The Current Frontier. In: Chua, Adamatzky (eds.) Chaos, CNN, Memristors and Beyond. World Scientific (forthcoming)

    Google Scholar 

  35. White, D.A., Sofge, D.A. (eds.): Handbook of Intelligent Control. Van Nostrand Reinhold, New York (1992)

    Google Scholar 

  36. Wonnacott, T.H., Wonnacott, R.J.: Introductory Statistics for Business and Economics, 4th edn. Wiley (1990)

    Google Scholar 

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Author information

Authors and Affiliations

  1. National Science Foundation and Center for Large-Scale Integration and Optimization of Networks (CLION), FedEx Institute of Technology, Memphis, TN, USA

    Paul J. Werbos

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  1. Paul J. Werbos
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Editors and Affiliations

  1. , Edificio de Investigación, European Centre for Soft Computing, C Gonzalo Gutiérrez Quirós S/N, Mieres, 33600, Spain

    Rudolf Seising

  2. Edificio de Investigación, 3ª Planta., European Centre for Soft Computing, C Gonzalo Gutiérrez Quirós S/N, Mieres, 33600, Asturias, Spain

    Enric Trillas

  3. Edificio de Investigación, 3ª Planta., European Centre for Soft Computing, Asturias, Mieres, 33600, Spain

    Claudio Moraga

  4. , Department of Mathematic and Informatics, Università di Palermo, Via Archirafi 34, Palermo, 90123, Italy

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Werbos, P.J. (2013). Fuzziness, Probability, Uncertainty and the Foundations of Knowledge. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35644-5_52

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  • DOI: https://doi.org/10.1007/978-3-642-35644-5_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35643-8

  • Online ISBN: 978-3-642-35644-5

  • eBook Packages: EngineeringEngineering (R0)

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